Reference

Abstract

"We simulate evaporation-driven self-assembly of colloidal crystals using an equivalent network model. Relationships
between a regular hexagonally close-packed array of hard, monodisperse spheres, the associated pore space, and
selectivity mechanisms for face-centered cubic microstructure propagation are described. By accounting for contact
line rearrangement and evaporation at a series of exposed menisci, the equivalent network model describes creeping
flow of solvent into and through a rigid colloidal crystal. Observations concerning colloidal crystal growth are interpreted
in terms of the convective steering hypothesis, which posits that solvent flow into and through the pore space of the
crystal may play a major role in colloidal self-assembly. Aspects of the convective steering and deposition of high-
Peclet-number rigid spherical particles at a crystal boundary are inferred from spatially resolved solvent flow into the
crystal. Gradients in local flow through boundary channels were predicted due to the channels’ spatial distribution
relative to a pinned free surface contact line. On the basis of a uniform solvent and particle flux as the criterion for
stability of a particular growth plane, these network simulations suggest the stability of a declining {311} crystal
interface, a symmetry plane which exclusively propagates fcc microstructure. Network simulations of alternate crystal
planes suggest preferential growth front evolution to the declining {311} interface, in consistent agreement with the
proposed stability mechanism for preferential fcc microstructure propagation in convective assembly."

Figure 1: (a)The two niches available for fluid flow through the {111} plane. Particles placed at the clear niches lead to fcc packing. (b) Convective colloidal assembly

Although colloidal crystals pack in an fcc structures through sedimentation, it is a mystery why colloidal crystals formed from convective assembly (Figure 1b) show the same structural tendency. Convective assembly is dominated by capillary and viscous forces and does not allow colloids to reach an equilibrium.

As proposed in an earlier paper by Norris, the fcc structure develops because of preferential flow patterns. As water evaporates from the crystal, it pulls in more colloids to the growing front (due to increasing capillary pressure at the surface of the crystal). As the particles flow towards the growing crystal, they see two kinds of niches (Figure 1a). Particle placement in the fcc niches extends the fcc crystal. This niche is not obstructed since there exists a clear path from the niche, to an octacoordinate pore body, and directly to the rest of the crystal (Figure 2d). The "twinning" niche, on the other hand, leads to divergence of the solvent flow through tetracoordinate connectivity.

The pore-network model developed in this paper allowed them to connect these microscopic ideas of flow with the macroscopic transport phenomena. The model did in fact support the idea that if the {111} face is the growing crystal plane, then one would see a preference for fcc packing due to solvent flow. However, the model also showed that with this tilt of an interface, one would not get a uniform growing front. Through further calculation, they found that the steady state growth plane would be the {311} plane of the crystal. This plane only supports the fcc growth niche, which would mean that it would inherently propagate the fcc structure. This is yet to be verified experimentally.

What this model did not address is the possible rearrangements that take place during assembly, and how van der Waals and electrostatic forces affect packing. This is probably very important in determining the final crystal structure. Until we really understand how convective assembly leads to an fcc crystal structure, we cannot manipulate the system to our advantage (and possibly force the crystal to pack into some other structure).